MATH SOLVE

4 months ago

Q:
# PLEASE HELP ASAP!A line is drawn so that it passes through the points (-3,-1) and (4,2). a. What is the slope of the line?b. Using the point (4,2) and the slope found above, write the equation of the line in point-slope form.Please write out how you got your answer or the steps you took.

Accepted Solution

A:

A) To find slope, use the equation:[tex]slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}} [/tex]where [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of one coordinate point , and [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of another coordinate point . Since we are given two coordinate points, (-3,-1) and (4,2), that means we can find the slope using the slope equation.

Let's choose (4, 2) as your [tex](x_{2}, y_{2})[/tex] point and (-3, -1) as your [tex](x_{1}, y_{1})[/tex] point, but you can switch those if you want! That makes [tex]x_{2} = 4, y_{2} = 2[/tex] and [tex]x_{1} = -3, y_{1} = -1[/tex]. Plug these values into the slope equation:

[tex]slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}} \\ slope = \frac{2-(-1)}{4-(-3)} \\ slope = \frac{3}{7} [/tex]

The slope of the line is 3/7.

B) Remember that the general equation for point-slope form is [tex]y - y_1 = m(x - x_1)[/tex], where m = the slope, [tex] x_{1}[/tex] = the x value of a coordinate point [tex](x_{1}, y_{2})[/tex] on the line, and [tex] y_{1} [/tex] = the y value of the same coordinate point on the line.

You are given (4, 2) as one of the coordinate points. That means [tex] x_{1}[/tex] = 4 and [tex] y_{1} [/tex] = 2. We found the slope, m = [tex] \frac{3}{7}[/tex] in part A. Now plug these values into the general equation for point-slope form to find your point-slope form equation:

[tex]y - y_1 = m(x - x_1)\\ y - 2 = \frac{3}{7}(x - 4)[/tex]

Your point-slope form equation is [tex]y - 2 = \frac{3}{7}(x - 4)[/tex].

Let's choose (4, 2) as your [tex](x_{2}, y_{2})[/tex] point and (-3, -1) as your [tex](x_{1}, y_{1})[/tex] point, but you can switch those if you want! That makes [tex]x_{2} = 4, y_{2} = 2[/tex] and [tex]x_{1} = -3, y_{1} = -1[/tex]. Plug these values into the slope equation:

[tex]slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}} \\ slope = \frac{2-(-1)}{4-(-3)} \\ slope = \frac{3}{7} [/tex]

The slope of the line is 3/7.

B) Remember that the general equation for point-slope form is [tex]y - y_1 = m(x - x_1)[/tex], where m = the slope, [tex] x_{1}[/tex] = the x value of a coordinate point [tex](x_{1}, y_{2})[/tex] on the line, and [tex] y_{1} [/tex] = the y value of the same coordinate point on the line.

You are given (4, 2) as one of the coordinate points. That means [tex] x_{1}[/tex] = 4 and [tex] y_{1} [/tex] = 2. We found the slope, m = [tex] \frac{3}{7}[/tex] in part A. Now plug these values into the general equation for point-slope form to find your point-slope form equation:

[tex]y - y_1 = m(x - x_1)\\ y - 2 = \frac{3}{7}(x - 4)[/tex]

Your point-slope form equation is [tex]y - 2 = \frac{3}{7}(x - 4)[/tex].